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• Printable Multiplying Polynomials Worksheet in PDF: FOIL and Area Model Practice

Printable Multiplying Polynomials Worksheet in PDF: FOIL and Area Model Practice

This free printable worksheet gives high school algebra students practice multiplying polynomials, from two binomials up to a binomial multiplied by a longer expression. Each problem asks students to write the answer in standard form, combining like terms as needed, and the worksheet includes an answer key.

Problems combine distributive-property multiplication with the addition and subtraction skills needed to simplify the result, building the foundation students need for factoring and quadratic equations. For more practice, you can explore different Brighterly’s algebra worksheets hub.

Multiplying Polynomials Worksheet: Free Download

This topic is available as three downloadable worksheet files:

How to Multiply Polynomials: FOIL and the Area Model

Multiplying polynomials means applying the distributive property so that every term in one polynomial is multiplied by every term in the other, then combining like terms. Two common methods make this process easier to organize: FOIL for two binomials, and the area (box) model for longer polynomials.

FOIL Method: Multiplying Two Binomials

FOIL stands for First, Outer, Inner, Last — the four pairs of terms to multiply when both polynomials are binomials.

Worked Example: (x + 3)(x + 5)

• First: x × x = x²
• Outer: x × 5 = 5x
• Inner: 3 × x = 3x
• Last: 3 × 5 = 15

Area Model: Multiplying a Binomial by a Longer Polynomial

When one polynomial has more than two terms, FOIL no longer applies directly, but the area (box) model still works: set up a grid with one polynomial’s terms across the top and the other’s terms down the side, multiply each pair, then add the results and combine like terms.

Worked Example: (x + 4)(x³ − 2x² + x − 5)

x	x³	−2x²	x	−5
x	x⁴	−2x³	x²	−5x
+4	4x³	−8x²	4x	−20

Adding every cell in the grid gives: x⁴ − 2x³ + x² − 5x + 4x³ − 8x² + 4x − 20. Combining like terms (−2x³ + 4x³, x² − 8x², and −5x + 4x) simplifies this to:

x⁴ + 2x³ − 7x² − x − 20

More Factoring and Polynomial Worksheets

Once your child is confident multiplying polynomials, explore more of Brighterly’s algebra practice:

• Multiplying Monomials and Polynomials Worksheets
• Factoring Polynomials Worksheets
• Factoring Trinomials Worksheets
• Factoring by Grouping Worksheets
• Factoring Quadratics Worksheets
• Greatest Common Factor Worksheets

What Students Practice With This Multiplying Polynomials Worksheet

• Multiplying two binomials using the FOIL method
• Multiplying a binomial by a longer polynomial using the area (box) method
• Applying the distributive property across multiple terms
• Combining like terms and writing results in standard form
• Checking work against an included answer key

Each worksheet includes an answer key, so students can check their own results without waiting for a teacher to grade the page. Practicing both FOIL and the area model gives students a method to fall back on no matter how many terms a polynomial has, rather than a single trick that only works for binomials.

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Frequently Asked Questions

What is the FOIL method for multiplying polynomials?

FOIL stands for First, Outer, Inner, Last, and it describes the order for multiplying two binomials: multiply the first terms, then the outer terms, then the inner terms, then the last terms, and add the four results together. After combining any like terms, the result is the product written in standard form.

What grade level is this multiplying polynomials worksheet for?

This worksheet is designed for high school algebra students, spanning grades 9 through 11, including students working through Algebra 2. Problems range from multiplying two binomials to multiplying a binomial by a longer polynomial, matching the level where students first build strong polynomial multiplication skills before moving on to factoring and quadratic equations.

How do you multiply a binomial by a polynomial with more than two terms?

Since FOIL only covers two binomials, a longer polynomial is best multiplied using the area, or box, method. Each term of one polynomial is multiplied by each term of the other in a grid, and then every result in the grid is added together and simplified by combining any like terms into one final expression.

Does this worksheet include an answer key?

Yes, this multiplying polynomials worksheet includes an answer key. Students can check their own results as soon as they finish a problem, which helps them catch mistakes in a FOIL or area-model step right away, instead of waiting for a teacher to grade the assignment before finding out what went wrong.

Is this multiplying polynomials worksheet free and printable?

Yes, this worksheet is free to download as a printable PDF, and no account or sign-up is required. Students can print the pages for hands-on practice with a pencil and paper, or work through the problems digitally if a printer isn’t available, since the questions work equally well either way.